Dynamics Of A Piecewise Continuous Infectious Disease SIQR Model And A SIR Model Of Network Virus Propagation

In this thesis,we study a SIQR epidemic model with discontinuous strategy and a class of internet virus SIR model with two thresholds.This thesis mainly applies the stability theory,qualitative theory of plane differential equations and the theory of righthand discontinuous differential equations,combines LaSalle invariant principle,the nonsmooth Ly apunov funtion.with Bendixson-Dulac criterion,even differential inequality technique,Filippov convex combination and Poincare map and so on.The text consists of four chapters.The background of the research,significance and development status of infectious disease model and computer virus model are given in Chapter 1,and the research contents of this thesis are briefly overviewed.In Chapter 2,we introduce some basic mathematical concepts and theoretical knowledges in this thesis.In the third chapter,from the perspective of disease prevention and control,we analyze a class of SIQR infectious disease model with isolation strategy.The global dynamic behaviors of the model are obtained by applying non-smooth Ly apunov functions,Poincare map and Filippov qualitative theory.In Chapter 4,an infectious disease model with two thresholds is considered.In the analysis of the global dynamics of the model,the Bendixson-Dulac criterion and Green’s formula are used to prove that there are no crossing limit cy cles in the model.The vector field analysis and Poincare map show that there are no sliding mode limit cycles in the model.Combined with the limit set theory,the global dynamic results of the model are obtained.In the end of the thesis,the researches are summarized and researches in the future are prospected.